In finance, an index is a statistical aggregate that usually refers to a measure of economic performance or market performance. For example, a stock market index is a method of measuring the value of a section of the stock market. Investors sometimes use stock indexes to describe market conditions, to benchmark investment results, or to construct portfolios. Index construction methodologies generally determine the relative contribution of each member to the overall index using equal weighting or some measure of market or fundamental data. Portfolios based on such indexes suffer from numerous disadvantages. For instance, in indexes weighted by market capitalization or a measure of fundamental size, a small number of constituents tend to have disproportionately large weight, thus introducing a degree of idiosyncratic risk. On the other extreme, equal weight indexes have horizontal weighting curves and give no extra weight to securities that may possess desirable characteristics as determined through various techniques of security analysis. Further, in market or fundamentals-based indexes, the difference in weights between constituents is uneven, leading to a lack of standardization between indexes or even in the same index over time. These conventional indexes are rigid, lacking any mechanism to alter their weighting percentage curves to resolve these structural limitations. Moreover, modern finance recognizes various risk factors, sometimes referred to as anomalies, which account for investment performance, such as the size, value, momentum, and low volatility effects. Existing indexes offer only incidental, narrow, and/or exclusionary access to these risk factors. Therefore, a distinct disadvantage is that these indexes fail to take advantage of a synergistic effect of holdings that are rich in multiple risk factors. Finally, portfolios based on these indexes require many separate funds to gain broad risk factor exposure, increasing complexity and costs associated with portfolio management. Existing methods cannot provide consistent, customizable, direct, and diversified exposure to the many investment risk factors in a single index.